{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:H4G7XAXVKUDF2E5UOXPCK77VVC","short_pith_number":"pith:H4G7XAXV","canonical_record":{"source":{"id":"2606.26784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2026-06-25T09:20:03Z","cross_cats_sorted":[],"title_canon_sha256":"bb3727009686f29f356f6ea4d42cc509f4e23482e9cd11dcda31af14c949ca68","abstract_canon_sha256":"8dadb5f6f9145cbe5e1f585b609af3dae8e7cb57a60230ebc0bf6e59702abf4a"},"schema_version":"1.0"},"canonical_sha256":"3f0dfb82f555065d13b475de257ff5a8b8848aed5a9a2fa46b72337c0d9ccc93","source":{"kind":"arxiv","id":"2606.26784","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26784","created_at":"2026-06-26T01:15:59Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26784v1","created_at":"2026-06-26T01:15:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26784","created_at":"2026-06-26T01:15:59Z"},{"alias_kind":"pith_short_12","alias_value":"H4G7XAXVKUDF","created_at":"2026-06-26T01:15:59Z"},{"alias_kind":"pith_short_16","alias_value":"H4G7XAXVKUDF2E5U","created_at":"2026-06-26T01:15:59Z"},{"alias_kind":"pith_short_8","alias_value":"H4G7XAXV","created_at":"2026-06-26T01:15:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:H4G7XAXVKUDF2E5UOXPCK77VVC","target":"record","payload":{"canonical_record":{"source":{"id":"2606.26784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2026-06-25T09:20:03Z","cross_cats_sorted":[],"title_canon_sha256":"bb3727009686f29f356f6ea4d42cc509f4e23482e9cd11dcda31af14c949ca68","abstract_canon_sha256":"8dadb5f6f9145cbe5e1f585b609af3dae8e7cb57a60230ebc0bf6e59702abf4a"},"schema_version":"1.0"},"canonical_sha256":"3f0dfb82f555065d13b475de257ff5a8b8848aed5a9a2fa46b72337c0d9ccc93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:15:59.610159Z","signature_b64":"TgiyB3wbWQyOI2AdlkPiP+6xpqsw1lsYqoGI3A5ONLp4Dek/k9vPmNWxtplXgHmklVySgpJE00CpbFBWdNbsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f0dfb82f555065d13b475de257ff5a8b8848aed5a9a2fa46b72337c0d9ccc93","last_reissued_at":"2026-06-26T01:15:59.609813Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:15:59.609813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.26784","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-26T01:15:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jcEIqKIOi4zNqSB0aqRH3jRJ2sz/lPpv3pWi0OnP0as0zLaVbMjJCOmaepBmXmbR4zei6ZW07Ftv+ot0wF2MBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:19:32.805478Z"},"content_sha256":"54a310faa585f077bdade9a5d325e63bc29bc630ad1b21dc90e70654cb0e214d","schema_version":"1.0","event_id":"sha256:54a310faa585f077bdade9a5d325e63bc29bc630ad1b21dc90e70654cb0e214d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:H4G7XAXVKUDF2E5UOXPCK77VVC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"MergeLLL: A Hierarchical Divide-and-Conquer Framework for LLL-Based Lattice Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Niharika Gauraha","submitted_at":"2026-06-25T09:20:03Z","abstract_excerpt":"Lattice basis reduction algorithms have various applications in computational number theory and lattice-based cryptography, but their complexity increases rapidly with the dimension. Motivated by the divide-and-conquer strategy of merge sort and incorporating PotLLL-style deep insertions during recombination, MergeLLL is proposed. In this framework, a lattice basis is split into sub-bases, local reductions are performed independently, and the full basis is reconstructed through hierarchical merging.\n  The approach is focused on improving local lattice structure first before global basis proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26784","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.26784/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-26T01:15:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AsfZRnIfOw1BeaaSnK3qrv8J5/2nKjL5JhpInXWkl3fcGmZ1j8Fd4/dGmxdooJbKyEIWYpTYsTU5EB+62Y9RBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:19:32.805870Z"},"content_sha256":"c437a543b746585269c01a0ca21fff19ae38339def8949c7ca22af84da67bf8e","schema_version":"1.0","event_id":"sha256:c437a543b746585269c01a0ca21fff19ae38339def8949c7ca22af84da67bf8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H4G7XAXVKUDF2E5UOXPCK77VVC/bundle.json","state_url":"https://pith.science/pith/H4G7XAXVKUDF2E5UOXPCK77VVC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H4G7XAXVKUDF2E5UOXPCK77VVC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T07:19:32Z","links":{"resolver":"https://pith.science/pith/H4G7XAXVKUDF2E5UOXPCK77VVC","bundle":"https://pith.science/pith/H4G7XAXVKUDF2E5UOXPCK77VVC/bundle.json","state":"https://pith.science/pith/H4G7XAXVKUDF2E5UOXPCK77VVC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H4G7XAXVKUDF2E5UOXPCK77VVC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:H4G7XAXVKUDF2E5UOXPCK77VVC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8dadb5f6f9145cbe5e1f585b609af3dae8e7cb57a60230ebc0bf6e59702abf4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2026-06-25T09:20:03Z","title_canon_sha256":"bb3727009686f29f356f6ea4d42cc509f4e23482e9cd11dcda31af14c949ca68"},"schema_version":"1.0","source":{"id":"2606.26784","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26784","created_at":"2026-06-26T01:15:59Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26784v1","created_at":"2026-06-26T01:15:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26784","created_at":"2026-06-26T01:15:59Z"},{"alias_kind":"pith_short_12","alias_value":"H4G7XAXVKUDF","created_at":"2026-06-26T01:15:59Z"},{"alias_kind":"pith_short_16","alias_value":"H4G7XAXVKUDF2E5U","created_at":"2026-06-26T01:15:59Z"},{"alias_kind":"pith_short_8","alias_value":"H4G7XAXV","created_at":"2026-06-26T01:15:59Z"}],"graph_snapshots":[{"event_id":"sha256:c437a543b746585269c01a0ca21fff19ae38339def8949c7ca22af84da67bf8e","target":"graph","created_at":"2026-06-26T01:15:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.26784/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Lattice basis reduction algorithms have various applications in computational number theory and lattice-based cryptography, but their complexity increases rapidly with the dimension. Motivated by the divide-and-conquer strategy of merge sort and incorporating PotLLL-style deep insertions during recombination, MergeLLL is proposed. In this framework, a lattice basis is split into sub-bases, local reductions are performed independently, and the full basis is reconstructed through hierarchical merging.\n  The approach is focused on improving local lattice structure first before global basis proper","authors_text":"Niharika Gauraha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2026-06-25T09:20:03Z","title":"MergeLLL: A Hierarchical Divide-and-Conquer Framework for LLL-Based Lattice Reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26784","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:54a310faa585f077bdade9a5d325e63bc29bc630ad1b21dc90e70654cb0e214d","target":"record","created_at":"2026-06-26T01:15:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8dadb5f6f9145cbe5e1f585b609af3dae8e7cb57a60230ebc0bf6e59702abf4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2026-06-25T09:20:03Z","title_canon_sha256":"bb3727009686f29f356f6ea4d42cc509f4e23482e9cd11dcda31af14c949ca68"},"schema_version":"1.0","source":{"id":"2606.26784","kind":"arxiv","version":1}},"canonical_sha256":"3f0dfb82f555065d13b475de257ff5a8b8848aed5a9a2fa46b72337c0d9ccc93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f0dfb82f555065d13b475de257ff5a8b8848aed5a9a2fa46b72337c0d9ccc93","first_computed_at":"2026-06-26T01:15:59.609813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:15:59.609813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TgiyB3wbWQyOI2AdlkPiP+6xpqsw1lsYqoGI3A5ONLp4Dek/k9vPmNWxtplXgHmklVySgpJE00CpbFBWdNbsAg==","signature_status":"signed_v1","signed_at":"2026-06-26T01:15:59.610159Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.26784","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54a310faa585f077bdade9a5d325e63bc29bc630ad1b21dc90e70654cb0e214d","sha256:c437a543b746585269c01a0ca21fff19ae38339def8949c7ca22af84da67bf8e"],"state_sha256":"b34a960465a2de85e2726df945f1fae1277ea5b78d2ba6af85033d5004176256"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nhZFsAdztCtkswgUXS6xCegSWmZOaEhf/zrgAOUKm1R8f/diNld+p7LKFwoCA64vnl7UXog4bjpbVlfNkfNICQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T07:19:32.808109Z","bundle_sha256":"31b0cc3d1e3ca1821027697fd8319623d585937dcf7c37156642b0530b0cb4c9"}}